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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Summability factors for Cesàro methods


Author: David F. Dawson
Journal: Proc. Amer. Math. Soc. 73 (1979), 371-374
MSC: Primary 40G05
MathSciNet review: 518523
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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that if each of r and s is a nonnegative integer and $ \{ {f_p}\} $ is a complex sequence such that $ \Sigma {f_p}{a_p}$ is Cesàro summable of order s whenever $ \Sigma {a_p}$ is Cesàro summable of order r, then $ \Sigma {f_p}{a_p}$ is Cesàro summable of order r whenever $ \Sigma {a_p}$ is Cesàro summable of order r.


References [Enhancements On Off] (What's this?)

  • [1] David F. Dawson, A generalization of a theorem of Hans Hahn concerning matrix summability, Boll. Un. Mat. Ital. (4) 3 (1970), 349–356. MR 0265813 (42 #722)
  • [2] Tetsuzo Kojima, On generalized Toeplitz's theorems on limit and their applications, Tôhoku Math. J. 12 (1917), 291-326.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0518523-2
PII: S 0002-9939(1979)0518523-2
Keywords: Cesàro summability, bounded variation, summability factors
Article copyright: © Copyright 1979 American Mathematical Society



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